org.apache.commons.math3.optimization.general
Class LevenbergMarquardtOptimizer

java.lang.Object
  org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
      org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
          org.apache.commons.math3.optimization.general.LevenbergMarquardtOptimizer

All Implemented Interfaces:

BaseMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>, BaseOptimizer<PointVectorValuePair>, DifferentiableMultivariateVectorOptimizer

Deprecated. As of 3.1 (to be removed in 4.0).

@Deprecated
public class LevenbergMarquardtOptimizer
extends AbstractLeastSquaresOptimizer

This class solves a least squares problem using the Levenberg-Marquardt algorithm.

This implementation should work even for over-determined systems (i.e. systems having more point than equations). Over-determined systems are solved by ignoring the point which have the smallest impact according to their jacobian column norm. Only the rank of the matrix and some loop bounds are changed to implement this.

The resolution engine is a simple translation of the MINPACK lmder routine with minor changes. The changes include the over-determined resolution, the use of inherited convergence checker and the Q.R. decomposition which has been rewritten following the algorithm described in the P. Lascaux and R. Theodor book Analyse numérique matricielle appliquée à l'art de l'ingénieur, Masson 1986.

The authors of the original fortran version are:

• Argonne National Laboratory. MINPACK project. March 1980
• Burton S. Garbow
• Kenneth E. Hillstrom
• Jorge J. More

The redistribution policy for MINPACK is available here, for convenience, it is reproduced below.

Minpack Copyright Notice (1999) University of Chicago. All rights reserved

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

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Since:

2.0

Version:

$Id: LevenbergMarquardtOptimizer.java 7721 2013-02-14 14:07:13Z CardosoP $

Field Summary

Fields inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer

cols, cost, objective, point, rows, weightedResidualJacobian, weightedResiduals

Fields inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer

evaluations

Constructor Summary

LevenbergMarquardtOptimizer()
Deprecated. Build an optimizer for least squares problems with default values for all the tuning parameters (see the other contructor.

LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
Deprecated. Constructor that allows the specification of a custom convergence checker.

LevenbergMarquardtOptimizer(double initialStepBoundFactor, ConvergenceChecker<PointVectorValuePair> checker, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated. Constructor that allows the specification of a custom convergence checker, in addition to the standard ones.

LevenbergMarquardtOptimizer(double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance)
Deprecated. Build an optimizer for least squares problems with default values for some of the tuning parameters (see the other contructor.

LevenbergMarquardtOptimizer(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated. The arguments control the behaviour of the default convergence checking procedure.

Method Summary

protected PointVectorValuePair

doOptimize() Deprecated. Perform the bulk of the optimization algorithm.

Methods inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer

computeCost, computeCovariances, computeResiduals, computeSigma, computeWeightedJacobian, getChiSquare, getCovariances, getCovariances, getJacobianEvaluations, getRMS, getWeightSquareRoot, guessParametersErrors, optimize, optimize, optimizeInternal, setCost, setUp, updateJacobian, updateResidualsAndCost

Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer

computeObjectiveValue, getConvergenceChecker, getEvaluations, getMaxEvaluations, getObjectiveFunction, getStartPoint, getTarget, getTargetRef, getWeight, getWeightRef, optimize, optimizeInternal, optimizeInternal

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.math3.optimization.BaseOptimizer

getConvergenceChecker, getEvaluations, getMaxEvaluations

Constructor Detail

LevenbergMarquardtOptimizer

public LevenbergMarquardtOptimizer()

Deprecated.

Build an optimizer for least squares problems with default values for all the tuning parameters (see the other contructor. The default values for the algorithm settings are:

• Initial step bound factor: 100
• Cost relative tolerance: 1e-10
• Parameters relative tolerance: 1e-10
• Orthogonality tolerance: 1e-10
• QR ranking threshold: Precision.SAFE_MIN

LevenbergMarquardtOptimizer

public LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)

Deprecated.

Constructor that allows the specification of a custom convergence checker. Note that all the usual convergence checks will be disabled. The default values for the algorithm settings are:

• Initial step bound factor: 100
• Cost relative tolerance: 1e-10
• Parameters relative tolerance: 1e-10
• Orthogonality tolerance: 1e-10
• QR ranking threshold: Precision.SAFE_MIN

Parameters:

checker - Convergence checker.

LevenbergMarquardtOptimizer

public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
                                   ConvergenceChecker<PointVectorValuePair> checker,
                                   double costRelativeTolerance,
                                   double parRelativeTolerance,
                                   double orthoTolerance,
                                   double threshold)

Deprecated.

Constructor that allows the specification of a custom convergence checker, in addition to the standard ones.

Parameters:

initialStepBoundFactor - Positive input variable used in determining the initial step bound. This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag * x if non-zero, or else to initialStepBoundFactor itself. In most cases factor should lie in the interval (0.1, 100.0). 100 is a generally recommended value.

checker - Convergence checker.

costRelativeTolerance - Desired relative error in the sum of squares.

parRelativeTolerance - Desired relative error in the approximate solution parameters.

orthoTolerance - Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.

threshold - Desired threshold for QR ranking. If the squared norm of a column vector is smaller or equal to this threshold during QR decomposition, it is considered to be a zero vector and hence the rank of the matrix is reduced.

LevenbergMarquardtOptimizer

public LevenbergMarquardtOptimizer(double costRelativeTolerance,
                                   double parRelativeTolerance,
                                   double orthoTolerance)

Deprecated.

Build an optimizer for least squares problems with default values for some of the tuning parameters (see the other contructor. The default values for the algorithm settings are:

• Initial step bound factor}: 100
• QR ranking threshold}: Precision.SAFE_MIN

Parameters:

costRelativeTolerance - Desired relative error in the sum of squares.

parRelativeTolerance - Desired relative error in the approximate solution parameters.

orthoTolerance - Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.

LevenbergMarquardtOptimizer

public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
                                   double costRelativeTolerance,
                                   double parRelativeTolerance,
                                   double orthoTolerance,
                                   double threshold)

Deprecated.

The arguments control the behaviour of the default convergence checking procedure. Additional criteria can defined through the setting of a ConvergenceChecker.

Parameters:

initialStepBoundFactor - Positive input variable used in determining the initial step bound. This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag * x if non-zero, or else to initialStepBoundFactor itself. In most cases factor should lie in the interval (0.1, 100.0). 100 is a generally recommended value.

costRelativeTolerance - Desired relative error in the sum of squares.

parRelativeTolerance - Desired relative error in the approximate solution parameters.

orthoTolerance - Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.

threshold - Desired threshold for QR ranking. If the squared norm of a column vector is smaller or equal to this threshold during QR decomposition, it is considered to be a zero vector and hence the rank of the matrix is reduced.

Method Detail

doOptimize

protected PointVectorValuePair doOptimize()

Deprecated.

Perform the bulk of the optimization algorithm.

Specified by:

doOptimize in class BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>

Returns:

the point/value pair giving the optimal value for the objective function.